I'm currently a sophomore in a state school, so obviously I'll be preparing for law school soon

I mean, not really. And by "state school" I'm assuming you mean a state university. The only preparation you can do for law school is intern with a lawyer to see if its perhaps something you want to do, otherwise, the only prep you need to do is kick the LSAT's ass. Just talk to as many lawyers as you can to get a feel for the profession, but honestly, even when you're in law school, you're still preparing for law school. It really is quite early though, so don't stress about it or put the cart before the horse.

What are some classes I can take in undergrad to help me do better in law school?

The only course I could recommend is a class on logic, usually taught by your philosophy department. I found that it helped for understanding parts of the LSAT, otherwise I don't think there's a course in college for law school per se. Maybe a political science class on understanding the various branches of government would be useful, but you could learn that on Wikipedia in a few hours.

LSAT? Is there anything you would have taken/done in undergrad that you think might benefit me?

Not at all, there's no substantive class in college that will help in law school. Law school is a whole other beast. What will help is having a very, very good work/study ethic, that's probably the most important thing. Front loading your work a bit so you don't have to cram at the end, keeping up on reading etc. But start talking to lawyers, like I said above, so you can get comfortable talking with professionals in the field you want to go into.

Any general advice on the next steps and getting ready for law school would be greatly appreciated.

Really the only thing is getting together your application materials and getting a good LSAT so you can get into a good school with a scholarship. Start getting friendly with professors if you haven't done that already, because they're your recommendation letters, and you don't want them sending out generic letters, you want them to know you. Most of my professors knew me from being a sophomore onwards, and they were able to track how much my work improved, and I believe they wrote me amazing letters or rec.

But you won't be doing that until your junior year, and you're a sophomore now. The time people take the LSAT is in the summer between their junior and senior year.

For the time being, concentrate on getting amazing grades for the rest of your sophomore year, and then over the summer start doing some networking.

There's also something to be said for getting some work experience between college and law school so that when you get to law school, it isn't just a continuation of college. I took a few years out, I perhaps didn't do a whole lot, but it put the fear into to me and I worked a lot during my first semester and ended up doing well, and I think some of my colleagues who were K-JD had the college mentality and it didn't work out.